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N taking surveys it is unnecessary and unusual to make a station at every angular point, because the field-work can be taken with much greater expedition, by using off-sets and intersections, and with equal certainty; especially where creeks, &c. bound the survey.
Off-sets are perpendicular lines drawn or measured from the angular points of the land, that lie on the right or left hand to the stationary distance, thus,
PL. II. fig. 2.
Let the black lines represent the boundaries of a farm or township: and let 1 be the first station; then if you have a good view to 2, omit the angular points between 1 and 2, and take the bearing and length of the stationary line 1, 2, and insert them in your field-book: but in chaining from I to 2, stop at d opposite the angular point a, and in your field-book insert the distance from 1 to d, which admit to be 4 C. 25L, as well as the measure of the off-set ad, which admit to be 1C.12L. thus: by the side of your field-book in a line with the first station, say at 4C. 25L. L. 1C. 12L. that is, at 4C. 25L. there is an off-set to the left hand of 1C. 12L.
This done, proceed on your distance line to e opposite to the angle b, and measure eb, supposing then 1 6 to be 70. 40L. and eb 3C. 40L. say (still in a line with the first station in your field-book) “ at 7C. 40L. L. 3C. 40L.” That is, at 7C. 40L. there is an off-set to the left of 3C. 40L. proceed then with your distance line to f opposite to the .angle c, and measure fc; suppose then if to be 13C. and fc 1C. 25L. say in the same line as before, at 13C. L. 1C. 25L. Then proceed from f to 2, ar 1 you will have the measure of the entire stationary line 1,2, which insert in its proper column by the bearing
In taking off-sets, it is necessary to have a perch chain, or a staff of half a perch, divided into links for measuring them; for by these means the chain in the stationary line is undisturbed, and the number of chains and links in that line from whence, or to which, the off-sets are taken, may be readily known.
Having arrived at the second station, if you find your view will carry you to 3, take the bearing from 2 to 3, and in measuring the distance line, stop at l opposite g; admit 21 to be 4C. 10L. and the off-set lg 1C. 20L. then in a line with the second station in your field-book, say at 4C. 10L. R. 1C. 20L. that is, the off-set is a right hand one of 1C. 20L. Again at m, which suppose to be 10C. 25L. from 2 ; take the off-set mh of 1C. 15L. and in a line with the second station, say at 10C. 25L. R. 1C, 15%. In the same line when you come to the boundary at i, insert the distance 2i, 13C. 10L. thus, at 130. 10L. 0; that is, at 13C. 10L. there is no ofi-set. At n, which is 15C. from 2, take the off-set nk 45L. and still opposite to the second station say at 15C. L. 45. L.
Let the line, 3, 6, represent the boundary, which by means of water, briers, or any other impediment, cannot be measured. In this case make one or more stations within or without the land, where the distances may be measured, and draw a line from the beginning of the first to the end of the last üistance, thus; make stations at 3, 4, and 5, taking the bearings, and measuring the distances .as usual, which insert in your field-book, and draw a mark like one side of a parenthesis, from the third to the fifth station, to shew thai a line drawn from the third station to the farthest end of the fifth stationary line will express the boundary. Thus,
No. Sta. Deg. Ch. L.
3 1721 5.45
Suppose the point p of the boundary to be inaccessible, by means of the lines 6p or p7, being overflowed, or that of a quarry, furze, &c. might prevent your taking their lengths : in this case take the bearing of the line 6, 7, which insert op-. posite to the sixth station in your field-book with the other bearing; then direct the index to the point p, and insert its bearings on the left side of the field-book, opposite to the sixth station, annexing thereto the words Int. for boundary; and have ing measured and inserted the distance 6, 7, set the index in the direction of the line 7p, and insert its bearing on the left of the seventh station of the field-book, annexing thereto the words Int. for boundary: the crossing or intersection of these iwo bearings will deterinine the point p, and of course the boundary 6p7 is also determined.
If your view will then reach in the first station,
take its bearing, stationary line, and off-sets, as before, and you have the field-book completed. Thus,
Remarks and intersect.
12L, at 7C. 40L. L.. 3C, 40L. at 13C. L. IC. 25L.
Close at the first station.
If you would lay down a tower, house, or any other remarkable object in its proper place; from any two stations take bearings to the object, and their intersection will determine the place where you are to insert it, in the manner that the tower is set out in the figure, from the intersection taken at the first and second stations of the above fieldbook.
A protraction of this will render all plain, on which lay off all your off-sets and intersections, and proceed to find the content by any of the methods in section the 4th.
The foregoing field-book may be otherwise kent,
R. hao. Remarks and intersection,
Cn. L. 318 Int. to a tower 1 358 1.12 4.25
7.40 1.25 13.00
How to cast up off-sets by the pen.
PL. 11. fig. 2.
1, 2-1f=2f - le=fe, le--id=ed. Then Id * ?dq=1da, by prob. 6, page 183, and $ cd x da+fc=bese, and 2f ^ $ fc=cf9; the sum